Question

If the height of a cylinder becomes $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ of the original height and the radius is doubled, then which of the following will be true?

• A. Total surface area of the cylinder will be doubled.
• B. Total surface area of the cylinder will remain unchanged.
• C. Total surface of the cylinder will be halved.
• D. None of the above.

Answer 1

The correct option is D

None of the above.

The explanation for the correct option:

Find the change in the total surface area of the cylinder.

Let the height of the cylinder be $\mathrm{h}$ and the radius be $\mathrm{r}$

Total Surface Area of the cylinder $=2\mathrm{\pi r}\left(\mathrm{h}+\mathrm{r}\right)$

If the height of the cylinder is $\frac{\mathrm{h}}{4}$and the radius is $2\mathrm{r}$

Thus, the Total Surface Area after changing dimension $=2\mathrm{\pi }\left(2\mathrm{r}\right)\left(\frac{\mathrm{h}}{4}+2\mathrm{r}\right)$

$$\begin{gathered} =4\mathrm{\pi r}\left(\frac{\mathrm{h}+8\mathrm{r}}{4}\right) \\ =\frac{4\mathrm{\pi r}\left(\mathrm{h}+8\mathrm{r}\right)}{4} \\ =\mathrm{\pi r}(\mathrm{h}+8\mathrm{r}) \end{gathered}$$

There is no direct relation in the Total Surface Area before and after changing dimensions.

Hence the correct option is (d)